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Chapter 4 Individual and Market Demand Chapter 4: Individual and Market Demand CHAPTER 4 INDIVIDUAL AND MARKET DEMAND EXERCISES 1. The ACME corporation determines that at current prices the demand for its computer chips has a price elasticity of -2 in the short run, while the price elasticity for its disk drives is -1. a. If the corporation decides to raise the price of both products by 10 percent, what will happen to its sales? To its sales revenue? We know the formula for the elasticity of demand is: %DQ E = . P %DP For computer chips, EP = -2, so a 10 percent increase in price will reduce the quantity sold by 20 percent. For disk drives, EP = -1, so a 10 percent increase in price will reduce sales by 10 percent. Sales revenue is equal to price times quantity sold. Let TR1 = P1Q1 be revenue before the price change and TR2 = P2Q2 be revenue after the price change. For computer chips: DTRcc = P2Q2 - P1Q1 DTRcc = (1.1P1 )(0.8Q1 ) - P1Q1 = -0.12P1Q1, or a 12 percent decline. For disk drives: DTRdd = P2Q2 - P1Q1 DTRdd = (1.1P1 )(0.9Q1 ) - P1Q1 = -0.01P1Q1, or a 1 percent decline. Therefore, sales revenue from computer chips decreases substantially, -12 percent, while the sales revenue from disk drives is almost unchanged, -1 percent. Note that at the point on the demand curve where demand is unit elastic, total revenue is maximized. b. Can you tell from the available information which product will generate the most revenue for the firm? If yes, why? If not, what additional information would you need? No. Although we know the responsiveness of demand to changes in price, we need to know both quantities and prices of the products to determine total sales revenue. 2. Refer to Example 4.3 on the aggregate demand for wheat in 1998. Consider 1996, at which time the domestic demand curve was QDD = 1560 - 60P. The export demand curve, however, was about the same as in 1998, i.e., QDE=1544-176P. Calculate and draw the aggregate demand curve for wheat in 1996. Given the domestic demand curve for wheat is QDD = 1560-60P, we find an intercept of 1560 1560 on the quantity axis and an intercept of = 26 on the price axis. The export 60 demand curve for wheat, QDE = 1544 - 176P, has an intercept of 1544 on the quantity 1544 axis and an intercept of = 8.77 on the price axis. The total demand curve follows 176 the domestic demand curve between the prices of $26 and $8.77 because the export demand is 0 in this range of prices. At $8.77 and a quantity of approximately 1033.7 = 1560 - (60)(8.77), the total demand curve kinks. As price drops below $8.77, total demand is domestic demand plus export demand, which is the horizontal sum of the two 41 Chapter 4: Individual and Market Demand individual demand curves. Between a price of $26 and $8.77 the equation for total demand is QT=1560-60P and between a price of $8.77 and zero, the equation for total demand is QT=QDD+QDE=3104-236P. See figure 4.2. P 26 8.77 QDE QT QDD Q 1544 1560 3104 Figure 4.2 5. Suppose you are in charge of a toll bridge that is essentially cost free. The demand for bridge crossings Q is given by P = 12 - 2Q. a. Draw the demand curve for bridge crossings. See figure 5.4a below. b. How many people would cross the bridge if there were no toll? At a price of zero, the quantity demanded would be 6. c. What is the loss of consumer surplus associated with the charge of a bridge toll of $6? The consumer surplus with no toll is equal to (0.5)(6)(12) = 36. Consumer surplus with a $6 toll is equal to (0.5)(3)(6) = 9, illustrated in Figure 4.4.a. Therefore, the loss of consumer surplus is $27. 42 Chapter 4: Individual and Market Demand Toll 12 10 8 Consumer Surplus 6 P = 12 - 2Q 4 2 Crossings 1 2 3 4 5 6 7 Figure 5.4.a 6.a. Orange juice and apple juice are known to be perfect substitutes. Draw the appropriate price-consumption (for a variable price of orange juice) and income- consumption curves. We know that the indifference curves for perfect substitutes will be straight lines. In this case, the consumer will always purchase the cheaper of the two goods. If the price of orange juice is less than that of apple juice, the consumer will purchase only orange juice and the price consumption curve will be on the “orange juice axis” of the graph. If apple juice is cheaper, the consumer will purchase only apple juice and the price consumption curve will be on the “apple juice axis.” If the two goods have the same price, the consumer will be indifferent between the two; the price consumption curve will coincide with the indifference curve. See Figure 4.6.a.i. Apple Juice PA < PO PA = PO E PA > PO U F Orange Juice Figure 4.6.a.i 43 Chapter 4: Individual and Market Demand Assuming that the price of orange juice is less than the price of apple juice, the consumer will maximize her utility by consuming only orange juice. As the level of income varies, only the amount of orange juice varies. Thus, the income consumption curve will be the “orange juice axis” in Figure 4.6.a.ii. Apple Juice Budget Constraint Income Consumption Curve U3 U2 U1 Orange Juice Figure 4.6.a.ii 5.b. Left shoes and right shoes are perfect complements. Draw the appropriate price- consumption and income-consumption curves. For goods that are perfect complements, such as right shoes and left shoes, we know that the indifference curves are L-shaped. The point of utility maximization occurs when the budget constraints, L1 and L2 touch the kink of U1 and U2. See Figure 4.6.b.i. Right Shoes Price Consumption Curve U2 U1 L1 L2 Left Shoes Figure 4.6.b.i In the case of perfect complements, the income consumption curve is a line through the corners of the L-shaped indifference curves. See Figure 4.6.b.ii. 44 Chapter 4: Individual and Market Demand Right Shoes Income Consumption Curve U2 U1 L1 L2 Left Shoes Figure 4.6.b.ii 7. Heather’s marginal rate of substitution of movie tickets for rental videos is known to be the same no matter how many rental videos she wants. Draw Heather’s income consumption curve and her Engel curve for videos. If we let the price of movie tickets be less than the price of a video rental, the budget constraint, L, will be flatter than the indifference curve for the substitute goods, movie tickets and video rentals. The income consumption curve will be on the “video axis,” since she only consumes videos. See Figure 4.7.a. Movie Tickets Income Consumption Curve L U3 U2 U1 Video Rentals Figure 4.7.a Heather’s Engel curve shows that her consumption of video rentals increases as her income rises, and thus the slope of her Engel curve is equal to the price of a video rental. See Figure 4.7.b. 45 Chapter 4: Individual and Market Demand Income + Price of Video + 1 Video Rentals Figure 4.7.b 8. You are managing a $300,000 city budget in which monies are spent on schools and public safety only. You are about to receive aid from the federal government to support a special anti-drug law enforcement program. Two programs that are available are (1) a $100,000 grant that must be spent on law enforcement; and (2) a 100 percent matching grant, in which each dollar of local spending on law enforcement is matched by a dollar of federal money. The federal matching program limits its payment to each city to a maximum of $100,000. a. Complete the table below with the amounts available for safety. 46 Chapter 4: Individual and Market Demand a. See Table 4.8.a. SCHOOLS SAFETY SAFETY SAFETY No Govt. Program (1) Program (2) Assistance $0 $300,000 $400,000 $400,000 $50,000 $250,000 $350,000 $350,000 $100,000 $200,000 $300,000 $300,000 $150,000 $150,000 $250,000 $250,000 $200,000 $100,000 $200,000 $200,000 $250,000 $50,000 $150,000 $100,000 $300,000 $0 $100,000 $0 Table 4.8.a b. Which program would you (the manager) choose if you wish to maximize the satisfaction of the citizens if you allocate $50,000 of the $300,000 to schools? What about $250,000? With $50,000 to schools and $250,000 to law enforcement, both aid programs yield the same amount, $100,000, so you are indifferent between the programs. With $250,000 to schools and $50,000 to law enforcement, program (1) yields $100,000 (for a total of $150,000) and program (2) yields $50,000 (for a total of $100,000), so you prefer program (1). c. Draw the budget constraints for the three options: no aid, program (1), or program (2). Schools 360 A C 300 Budget Constraints: 1. No federal aid, AB 240 2. Program 1, ACE D 3. Program 2, ADE 180 120 60 B E Safety 60 120 180 240 300 360 420 Figure 4.8.c 47 Chapter 4: Individual and Market Demand With no aid, the budget constraint is the line segment AB, from $300,000 for schools and nothing for law enforcement to $300,000 for law enforcement and nothing for schools.
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